The maximum volume of a right circular cylinder if the sum of its radius and height is $6 \text{ m}$ is: (in $\pi \text{ m}^3$)

An enemy fighter jet is flying along the curve given by $y = x^2 + 2$. $A$ soldier is placed at $(3, 2)$ and wants to shoot down the jet when it is nearest to him. The nearest distance is:

If the extreme value of the function $f(x) = \frac{4}{\sin x} + \frac{1}{1 - \sin x}$ in the interval $[0, \frac{\pi}{2}]$ is $m$ and it exists at $x = k$,then $\cos k =$

$A$ rectangle has one side on the positive $y-$ axis and one side on the positive $x-$ axis. The upper right hand vertex lies on the curve $y = \frac{\ln x}{x^2}$. The maximum area of the rectangle is

If $x = 1$ is a critical point of the function $f(x) = (3x^{2} + ax - 2 - a)e^{x}$,then

$A$ stone is thrown vertically upwards from the top of a tower $64 \ m$ high according to the law $s=48t-16t^{2}$. The greatest height attained by the stone above the ground is (in $m$)